We examine the extent to which observations from the Greenland ice sheet combined with three-dimensional dynamical ice sheet models and semi-Lagrangian tracer methods can be used to constrain inferences of the Eemian evolution of the ice sheet, of the extent and frequency of summit migration during the 100 kyr ice age cycle, and of the deep geothermal flux of heat from the Earth into the base of the ice sheet. Relative sea level, present-day surface geometry, basal temperature, and age and temperature profiles from the Greenland Ice Project (GRIP) are imposed as constraints to tune ice sheet model and climate forcing parameters. Despite the paucity of observations, model-based inferences suggest a significant northeast gradient in geothermal heat flux. Our analyses also suggest that during the glacial cycle, the contemporaneous summit only occupied the present-day location during interglacial periods. On the basis of the development and use of a high-resolution semi-Lagrangian tracer analysis methodology for δ18O, we rule out isotropic flow disturbances due to summit migration as a possible source of the high Eemian variability of the GRIP δ18O record. Finally, in contrast with results obtained in some recent attempts to infer the extent to which Greenland may have contributed to the anomalous highstand of Eemian sea level, we find that conservative bounds for this contribution are 2--5.2 m, with a more likely range of 2.7--4.5 m.